iv done this problem will somebody go over it for me and tell me if im doing it right thank u
picture is attached

Question

iv done this problem will somebody go over it for me and tell me if im doing it right thank u 
picture is attached

anonymous · Answer

attachment

anonymous · Answer

What's the height of the triangle, or the length of the hypotenuse?

anonymous · Answer

I need one of those to solve the problem.

anonymous · Answer

yeah but everything is in the picture 
i solved everything in the picture

tkhunny · Answer

It looks okay.  I'm not sure I can see all of your workings.  One thing I would suggest is a little simplification.  When you found that sides of the triangular section...

$x^{2} + x^{2} = 16^{2}$

$2x^{2} = 16^{2}$

$x^{2} = \dfrac{16^{2}}{2}$

$x = \dfrac{16}{\sqrt{2}} = 8\cdot\sqrt{2}$

This is so much nicer than that $\sqrt{128}$ you were floating around.  My goal is to try not to make any worse numbers than those with which I started.  I started with 16 and that was as bad as it got.

anonymous · Answer

so when we divide both sides by two and we take the square root of both sides i shouldnt simplify it further?

tkhunny · Answer

That's not what I'm saying.  When you did it. you did this:

$2x^{2} = 16^2$

$2x^{2} = 256$

$x^{2} = 128$

$x = \sqrt{128}$

$x = 11.31...$

The worst number I saw was 16.  You went all the way to 256!

It's not a matter of getting the right answer or not.  It's a matter of making your life easier and keeping things as simple as possible.  This will help you develop a more reliable style.

anonymous · Answer

yes thats true but in the end if we dont get the right answer points would be cut off lol i show more work so the teacher knows where i got my answer from

phi · Answer

It looks good.  The only improvement is you could have used short cuts.

First,  the top triangle is a 45-45-90 triangle ( you know because it has a right angle, and 2 = sides).   that means the hypotenuse is sqrt(2)*x   
In this case, 16= sqrt(2)x  and x= 16/sqrt(2).  the area is 1/2 * x^2 = 1/2 *16*16/2= 64

Or, you could notice that an altitude dropped from the 90 angle forms a new 45-45-90 triangle, with 2 equal sides.  Its sides will be 8.   That means the altitude is 8, and the area of the triangle is 1/2 * 16 * 8= 64

anonymous · Answer

will do next time im a little slow on catching these things thanks everybody for showing me that :)